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A2 Astrophysics 5.5.1(c)5.5.1(d)5.5.1(g)5.5.2(h)3.9.2.2(c)
~15 min Difficulty: 7/10 10 marks
Prior knowledge Absolute magnitudeStefan-Boltzmann lawHR diagram
Diagram description
A sketch of a Hertzsprung-Russell diagram with axes labelled luminosity/absolute magnitude and temperature/spectral class, showing the main sequence and the positions of the Sun and the red giant.
Problem structure
Part (a): magnitude difference and luminosity ratio (2 marks). Part (b): radius ratio from Stefan-Boltzmann law (3 marks). Part (c): HR diagram locations (2 marks). Part (d): stellar evolution of a Sun-like star (3 marks).

PhysicsUK Solve

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The Sun has absolute magnitude +4.8 and surface temperature 5800 K. A distant star has absolute magnitude −4.2 and surface temperature 3500 K.
(a) 2 marks
Calculate the difference in absolute magnitude and hence the ratio of the luminosities of the two stars.
(b) 3 marks
Use the Stefan-Boltzmann law to calculate the ratio of the radius of the distant star to the radius of the Sun.
(c) 2 marks
State where each star would be located on a Hertzsprung–Russell diagram.
(d) 3 marks
Describe the likely future evolution of a star similar to the Sun from the main sequence to its final state.
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